Factor each trinomial, if possible. See Examples 3 and 4. 4x^2y^2...

Question

Factor each trinomial, if possible. See Examples 3 and 4. 4x^2y^2+28xy+49

Accepted Answer

Welcome back. I am so glad you're here. We are given this polynomial nine M squared, N squared plus 48 M N plus 64. And we are asked to factor this polynomial. Well, typically when we start factoring, we're going to take a look at the first term and we're going to say what times what gives us that. But this time, we've got a nine M squared N squared and that's a lot of squared squares. Nine is three squared, M squared is M squared and N squared is N squared. We could also write this in parentheses three times M times N Squared. Very interesting. And then after we look at what times what goes into that first term, we look at the last term here and we say what times what goes into that and look, it's another squared 64 is eight squared. So when we've got a lot of squares, sometimes it fits this condition where we have X squared plus two X Y plus Y squared. And when that's the case, we can factor it much more quickly because that is equal to parentheses X plus Y squared. So let's see if it fits this condition. So we are X squared, R X would be three M N R Y for Y squared. Well, R Y would be equal to eight. And now let's see if we have two X Y, two times, our X is three M N and R Y is 82 times three times eight. That is 48. Bring down that M N and yes, this does match what we have in the middle. So we do meet this condition and we can factor it by setting this equal to parentheses X plus Y squared. While our X is three M N plus R Y is eight. And so this is our polynomial fully factored. We look at our answer choices and this matches with answer choice. B well done. We'll catch you on the next one.

Factor each trinomial, if possible. See Examples 3 and 4. 4x^2y^2+28xy+49

Key Concepts

Factoring Trinomials

Perfect Square Trinomials

Common Factors

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